A sample of at least 68 bulbs is needed to be 96% confident that our sample mean will be within 10 hours of the true mean.
What do you mean by sampling?
Sampling is the process of choosing the group from which you will actually collect data for your study. For instance, you could interview a sample of 100 students if you were examining the viewpoints of students at your university. With the help of sampling, you can test a statistical hypothesis on the features of a population.
According to the question,
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha =\frac{1-0.96}{2} =0.02[/tex]
Now, we have to find z in the Z table as such z has a p value of [tex]1-\alpha[/tex].
So it is z with a p value of [tex]1-0.02=0.98[/tex], so z= 2.055
Now, find the margin M as such
M = z*σ/√n
In which σ is the standard deviation of the population and n is the size of the sample.
In this problem, we have that:
σ = 40, M = 10,
M = z*σ/√n
[tex]10=2.055*\frac{40}{\sqrt{n} } \\10\sqrt{n}=82.2\\ \sqrt{n}=8.22\\ n=67.6[/tex]
Therefore, a sample of at least 68 bulbs is needed to be 96% confident that our sample mean will be within 10 hours of the true mean.
To learn more about sampling, visit:
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